Which fraction, in lowest terms, is equivalent to the decimal 0.5?
2 answers:
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Without any calculations it's evident it can't be neither B (both numbers are even, so they're divisible by 2) nor C (the numbers end in 0 and 5, so they're divisible by 5).
A.
Both numbers have a factor of 3, so they're not relatively prime.
That means it must be D. But, let's check it.
Indeed, those two numbers are relatively prime.
A.
Both numbers have a factor of 3, so they're not relatively prime.
That means it must be D. But, let's check it.
Indeed, those two numbers are relatively prime.
Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3. Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4. SAS criterion for congruence
5. Corresponding angles of congruent triangles are congruent
6. Converse of alternate interior angle theorem
7. Vertical angle theorem
8. SAS criterion for congruence
9. Converse of alternate interior angle theorem
As, , so
as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".